Languages first need to be practical. Allow me to make productive desktop, mobile and web-apps with Common Lisp with minimal setup and headache and I'll become a Common lisp fanatic the next day.
I have been doing desktop applications using Qtools[0] which is relatively pleasant to work with. I have prepared a hello-world kind of Qtools project[1] that is automatically built and released into ZIP files using Travis CI. (I haven't looked at it for a while and it seems that the configuration for one of the OSes needs a bit of an update due to a change in the directory structure of SBCL releases there, but the rest works.)
I don't have much experience with web applications in Lisp, but there's some substantial tooling there and I know of people who have done that before, both client- and server-wise.
I have no experience whatsoever about Common Lisp on mobile.
Web is a solved issue in most programming languages and Common Lisp is not the exception here.
The situation with desktop apps is pretty good. You have two commercial solutions and the usual open source bindings to popular libraries to choose from. There's also McCLIM if you fancy doing some archeology. https://github.com/CodyReichert/awesome-cl#gui
Concerning mobile, there is a LispWorks runtime, a subset of Common Lisp called mocl and there's also the option to use ECL. These need a bit of tinkering, as is usual for non platform languages.
McCLIM is not a domain of archaeology anymore; it has been seeing lots of development recently[0].
As for demonstrating it, two of the recent Online Lisp Meeting[1] videos utilize McCLIM: one of them describes Clouseau, an inspector application written in McCLIM[2] (running on the Mezzano OS as well[3], since McCLIM runs there too!) and the other utilizes McCLIM to visualize the functioning of Eclector, a portable and conforming implementation of the Common Lisp reader[4].
